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Mathematics

Gopal has a cumulative deposit account and deposits ₹ 900 per month for a period of 4 years. If he gets ₹ 52020 at the time of maturity, find the rate of interest.

Banking

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Answer

Let rate of interest be x%.

Given,

P = ₹ 900, n = (4 × 12) = 48 months, r = x%.

I = P×n(n+1)2×12×r100P \times \dfrac{n(n + 1)}{2 \times 12} \times \dfrac{r}{100}

∴I=₹900×48×492×12×x100=₹900×49x50=₹882x\therefore I = ₹ 900 \times \dfrac{48 \times 49}{2 \times 12} \times \dfrac{x}{100} \\[1em] = ₹ 900 \times \dfrac{49x}{50} \\[1em] = ₹ 882x

Sum deposited = ₹ 900 × 48 = ₹ 43200

Interest = Maturity value - Sum deposited = ₹ 52020 - ₹ 43200 = ₹ 8820.

⇒882x=8820⇒x=8820882⇒x=10%.\Rightarrow 882x = 8820 \\[1em] \Rightarrow x = \dfrac{8820}{882} \\[1em] \Rightarrow x = 10\%.

Hence, the rate of interest is 10% per annum.

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